A Grownups' Guide to Reasoning Through Single-Digit Addition Facts
Addition and subtraction facts should not be learned through memorization alone. If we focus only on memorization, there are 200 single-digit addition and subtraction facts children would need to memorize.
Instead, we want children to build fluency with these facts, which means that children are able to come up with the answers to these single-digit facts flexibly, accurately, and efficiently.
Fluency often leads to memorization down the road. But it doesn’t start there. It starts with reasoning and number sense. And these reasoning and number sense strategies are things we start building in preschool and kindergarten.
According to Teaching Student-Centered Mathematics by John Van de Walle, there are three phases children move through as they build fluency with single-digit facts.
Counting Strategies: Children count to add and subtract. Example: A child solves 5+4 by starting at 5 and counting up 4 more: 6, 7, 8, 9.
Reasoning Strategies: Children use their understanding of number relationships (number sense) to figure out addition and subtraction. Example: A child solves 5+4 by reasoning that 5+5=10 but they’re adding one less so the answer must be one less than 10, which is 9.
Fluency: Children are able to efficiently and accurately come up with the answer to a basic addition and subtraction fact.
⭐️ How does fluency differ from memorization? A child who has fluency with 5+4 might answer, “I just know,” when asked how they came up with the answer and this sounds the same as a child who has memorized it. But if you ask a child with fluency to explain it to a child who doesn’t know it, they’ll be able to explain it using a reasoning strategy, “See this ten frame? If it were full it would be 5+5=10, but it’s one less because it’s 5+4 so it’s 9.”
All three of these phases are important in the development of fluency, the issue arises when we jump straight from counting strategies to pushing for immediate recall. (Ex: A child can count to solve 5+4 and then we mistakenly move to memorizing 5+4=9 next.)
By doing this, we skip the reasoning stage and, in turn, limit children’s ability to apply single-digit facts to more advanced math concepts down the road.
The attachment below is meant to serve as a guide for grownups to help you understand the addition strategies your children are learning in early elementary so that you can support them on their homework and through conversations at home.
It is a summary of one piece in a much bigger conversation around fact fluency, but hopefully it will help you turn a homework moment of:
😩 “What do you mean you’re supposed to only use the doubles plus one strategy on this problem?? What is that?”
into
🤩 “Oh, you talked about the doubles plus one strategy at school today. Can you show me?”
🤓 And then you could even add, “It’s so cool how many ways we can learn to think about these problems! My brain also thought about….”
Strategies included:
Adding zero
One more/one less
Two more/two less
Combinations that make 10
One less than 10
Doubles
Doubles plus one
Doubles minus one
Make doubles
Make 10
References:
Van de Walle, J., Lovin, L., Karp, K., & Bay-Williams, J. (2018). Teaching student-centered mathematics. New York, NY: Pearson. https://www.pearson.com/us/higher-education/program/ Van-de-Walle-Teaching-Student-Centered-Mathematics- Developmentally-Appropriate-Instruction-for-Grades-Pre-K-2- Volume-I-with-Enhanced-Pearson-e-Text-Access-Card- Package-3rd-Edition/PGM270543.html